(CNN) -- A Connecticut woman attacked Monday by her friend's pet chimpanzee was taken Thursday from a Connecticut hospital to the famed Cleveland Clinic in Ohio, a hospital spokeswoman said. She would not divulge the victim's condition nor the reason for the move.

Travis, seen here as a younger chimp, was fatally shot by police after attacking Nash, authorities say.

Charla Nash, 55, was transferred by airplane and ambulance to the clinic, where doctors in December performed the first facial transplant in the United States.

The attack has raised questions about whether exotic animals should be kept as pets. Connecticut Attorney General Richard Blumenthal said Wednesday that primates and crocodiles should be added to a state list of animals citizens are not allowed to own.

Nash initially was taken to Stamford Hospital, where she underwent seven hours of surgery after she was attacked by the 14-year-old chimp, named Travis.

Nash's friend, Sandra Herold, 70, had called Nash for help in getting the animal back inside her house after he used a key to escape.

When Nash arrived at Herold's Stamford home, the chimp, who has been featured in TV commercials for Coca-Cola and Old Navy, jumped on her and began biting and mauling her, police said.